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A173280 First column of the matrix power A173279(.,.)^j in the limit j->infinity. 3
1, 1, 3, 7, 29, 129, 757, 5185, 41155, 368351, 3671635, 40295943, 482758111, 6268066531, 87668492115, 1314023850727, 21011431917453, 357014074280785, 6423561495057421, 122004755658629081, 2439367774898883497, 51213663674167659301, 1126452985959434543237 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

We can generalize A173279 to other matrices derived from some sequence S by Smat(n,k) := S(n-r*k), r >=2,

and find that they define sequences B(x) via S(x)= B(X)/B(x^r), b(n) = sum_{t=0..n, n-t =0 (mod r)} S(t)*B_{(n-t)/r} .

This here is the case of S=A000142 and r=2.

LINKS

Table of n, a(n) for n=0..22.

FORMULA

A000142(x) = A(x)/A(x^2), where A(x) and A000142(x) are the o.g.f.'s associated with A000142 and this sequence here.

sum_{n>=0} 1/a(n) = 2.519966353393413186683398448854995831308...

a(n) = (A173279^j)(n,0).

a(n) = sum_{t=0..n, n-t even} t!*a_{(n-t)/2}. [R. J. Mathar, Feb 22 2010]

MAPLE

A173280 := proc(n) option remember; local a, l; if n = 0 then 1; else a :=0 ; for l from n to 0 by -2 do a := a+ l!*procname((n-l)/2) : end do ; a ; end if; end proc:

seq(A173280(n), n=0..60) ; # R. J. Mathar, Feb 22 2010

CROSSREFS

Cf. A000142

Sequence in context: A110613 A088095 A217576 * A141477 A211371 A294383

Adjacent sequences:  A173277 A173278 A173279 * A173281 A173282 A173283

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Feb 14 2010

EXTENSIONS

Extended by R. J. Mathar, removed invalid comment on convergence to e. Feb 22 2010

Corrected index of B in the convolution formula in the comment - R. J. Mathar, Mar 23 2010

STATUS

approved

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Last modified November 18 09:06 EST 2017. Contains 294873 sequences.